All calculatorsAtom Economy Calculator
Compute atom economy (%) from a balanced reaction and a chosen desired product. Shows waste fraction and step-by-step calculation, with an optional mini donut chart.
Background
Atom economy measures how much of the reactants’ mass ends up in the desired product. For a balanced reaction aA + bB → pP + qQ + …, the atom economy toward P is (p·M(P)) / (a·M(A) + b·M(B)) × 100%. Higher values indicate “greener” processes with less waste.
How to use this calculator
- Balanced equation: Enter reactants, an arrow (
->or=>), and products with coefficients. - Desired product: Type the formula you consider the “target” (we auto-detect its coefficient on the product side).
- Output: Atom economy (%), waste fraction (%), full molar-mass breakdown, and optional chart.
Formula & Equation Used
Atom Economy (%): \( \frac{\nu_{\text{prod}} M_{\text{prod}}}{\sum_i \nu_i M_i \text{ (reactants)}} \times 100\% \)
Waste (%): \( 100\% - \text{Atom Economy} \)
Molar mass (M): Sum of atomic masses based on the chemical formula.
Example Problems & Step-by-Step Solutions
Example 1 — Aspirin synthesis
C₇H₆O₃ + C₄H₆O₃ → C₉H₈O₄ + C₂H₄O₂ (desired: C₉H₈O₄). Compute Σ(νM) for reactants and p·M for aspirin, then %.
Example 2 — Ammonia (Haber–Bosch)
N₂ + 3H₂ → 2NH₃ (desired: NH₃). Use 2·M(NH₃) over [1·M(N₂)+3·M(H₂)], ×100%.
Frequently Asked Questions
Q: Do I need a balanced equation?
Yes—coefficients scale molar masses. Unbalanced inputs give misleading atom economies.
Q: What if multiple desired products exist?
Choose one target at a time. Change “Desired product” and recompute to compare alternatives.
Q: Is atom economy the same as percent yield?
No. Atom economy is a theoretical mass-efficiency metric; percent yield is experimental efficiency.
